Temperature excursion: difference between revisions
Diff·revision 12 → 13·11:19, 28 Jul 2025
Difference between revision 12 and revision 13 of Temperature excursion. 9 lines changed; the page grew by 1,075 bytes.
| Revision 12 — 13:47, 18 Jul 2025 MicrodoseMagnus (talk) close an unbalanced quotation mark 12,339 bytes +574 | Revision 13 — 11:19, 28 Jul 2025 SPPS_Sorrel (talk) expand §Definition and framing 13,414 bytes +1,075 | ||
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| 79 | which lies inside the labelled range. The mean kinetic temperature, however, weights by degradation. With T = 295.15 K and 278.15 K: | 79 | which lies inside the labelled range. The mean kinetic temperature, however, weights by degradation. With T = 295.15 K and 278.15 K: |
| 80 | 80 | ||
| + | 81 | {{math|e^{−10000/295.15} = e^{−33.8811}}} and {{math|e^{−10000/278.15} = e^{−35.9518}}} | |
| + | 82 | ||
| + | 83 | The colder term is smaller by a factor of e<sup>−2.0707</sup> = 0.1261. The weighted sum is therefore | |
| + | 84 | ||
| + | 85 | === Why the two means diverge === | |
| + | 86 | The divergence is a direct consequence of convexity. Degradation rate is a convex function of temperature, so the average of the rates at two temperatures exceeds the rate at their average temperature. Mean kinetic temperature is defined as the temperature whose rate equals the average rate, and therefore always lies at or above the time-weighted arithmetic mean, with equality only for a constant profile. | |
| + | 87 | ||
| + | 88 | The gap widens with the spread of the profile. For the 30-day case above, a spread of 17 °C produced a gap of 2.9 °C. For the extreme cycle worked at [[Cold chain]], a spread of 28 °C produced a gap of 8.1 °C. A record with a narrow spread can be summarised by its arithmetic mean with little error; a record with a wide spread cannot, and it is precisely the wide-spread records that arise from excursions.{{r|haynes1971}} | |
| + | 89 | ||
| 81 | == References == | 90 | == References == |
| 82 | {{reflist}} | 91 | {{reflist}} |